Is it possible to add noise or other type of texture between color ramp stops?
It's time to dig this up and make it right.


Final



Object and UV Map

Create your horn using chosen technique and UV Unwrap it with Follow Active Quads as in my answer here: How to Straighten Curved UVs into Straight Belt

Using this method is somewhat crucial as we need to have UV Map straighten to X axis. 



Material

Extending a bit setup from your link we will make 3 maps. Base color, Roughness and Normal than use them with Principled Shader.

For Base color we mix main gradient with light and dark spots.

For Roughness and Normal we will use stretched and mixed Noise Textures.



Most important things here are Mapping nodes with stretching along X and Y axis.